I am having trouble understanding degrees of freedom concept with sample covariance. If df is equal to n minus the number of parameters estimated in the calculation, why doesn’t the the calculation of sample covariance involve n-2 since we are estimating the mean for two variables?

Thinking about this more, is df related not to the number of estimated parameters but to the number of estimated independent parameters? And because the value of Y is dependent on the value of X, we need not remove another degree of freedom?

Degrees of Freedom is about the distribution of the test statistic in which you usually would be using n - 2 df. The n-1 in the denominator is about eliminating bias.